SchedulingComplexConstructionPrograms
YuhongWang,P.E.1;YunLe2;andJiukunDai3
Abstract:Acomplexconstructionprogramusuallyconsistsofagroupofinterrelatedprojectswithdifferentlevelsofimportanceanddegreesofcertainty.Currently,timemanagementofaconstructionprogramusesthesametechniquesasthoseforasingleproject,andthemostcommonlyusedtechniqueisthecriticalpathmethod(CPM).However,theCPMmethodlacksflexibilityinhandlinguncertaintiesandoptions,adesirablefeatureinmanagingcomplexprograms.Thispaperproposesanewschedulingmethodthatisdrawnfromtheauthors’experiencesofmanagingalarge-scaleconstructionprogram—theShanghaiExpofacilityconstruction.ThenewmethodisdevelopedonthebasisofthetraditionalCPMmethodbutisabletoincorporateoptionsandimportancelevelsintotheprogramschedule.ThetheoreticalbasisandcalculationmethodofthisnewschedulingtechniquearediscussedinthecontextofmanagingtheShanghaiExpofacilityconstructionprogram.Thispapercontributestothebodyofknowledgeinconstructionmanagementbydevelopinganewschedulingtechniquewithprovenapplications.DOI:10.1061/(ASCE)ME.1943-5479.0000349.©2014AmericanSocietyofCivilEngineers.Authorkeywords:Projectmanagement;Scheduling;Criticalpathmethod;Constructioncosts;Control.
Downloaded from ascelibrary.org by Tongji University on 10/12/15. Copyright ASCE. For personal use only; all rights reserved.Introduction
Althoughthetermsprojectandprogramaresometimesusedinter-changeably(e.g.,BarrieandPaulson1992)inthecontextofcon-structionmanagement,theyarenowoftentreatedasdifferentconcepts.AccordingtotheProjectManagementInstitute(PMI),aprogramis“agroupofrelatedprojectsmanagedinacoordinatedmannertoobtainbenefitsandcontrolnotavailablefrommanagingthemindividually”(PMI2008).Similardefinitionsofprogramhavebeenprovidedinothersources(e.g.,Arttoetal.2009;Sanghera2008;Wagner2009).Inconstruction,itisnotuncommonforagroupofprojectstobeimplementedsimultaneously,andtheremovalofoneormoreprojectsfromthegroupmaynotseriouslyaffecttheoverallprogramgoals.Hence,itismoreappropriatetorefertothegroupofprojectsasaprograminsteadofasingle,largeproject.ExamplesofconstructionprogramsincludetheMeasureRintheUnitedStates(LAMetropolitanTransportationAuthority2012)andthe2010ShanghaiExpofacilityconstructionprograminChina.Theformerconsistsofdozensoftransitandhighwayprojectswithestimatedcoststotaling$40billion,whilethelatterconsistsofmorethan400buildingsinadditiontomanyurbaninfrastructures.
Althoughprogramsarecommonlyencounteredinconstruction,researchonprogrammanagementisrelativelyrecentandscarce,comparedwiththelargeamountofresearchonproject
AssitantProfessor,Dept.ofCivilandStructuralEngineering,HongKongPolytechnicUniv.,HungHom,HongKong(correspondingauthor).E-mail:ceyhwang@polyu.edu.hk2
ChairandProfessor,Dept.ofConstructionManagementandRealEstate,TongjiUniv.,Shanghai,China;andGeneralProgramManagerfortheShanghaiExpoConstructionProgram,ShanghaiKeruiInc.,Shanghai,China3
PerformanceEngineer,FLUOR,100FluorDanielDr.,C502,Greenville,SC29607
Note.ThismanuscriptwassubmittedonApril23,2014;approvedonOctober22,2014;publishedonlineonDecember3,2014.Discussionper-iodopenuntilMay3,2015;separatediscussionsmustbesubmittedforindividualpapers.ThispaperispartoftheJournalofManagementinEngineering,©ASCE,ISSN0742-597X/04014098(10)/$25.00.
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management.Moreover,thelimitedliteratureonprogrammanage-mentmainlyfocusesonconceptual,organizational,andbehavioralissues.Researchonfundamentalandpracticalmethodologiesforeffectiveprogrammanagementislacking.Asaresult,programmanagementtodaystillheavilyreliesonthetraditionaltechniquesforprojectmanagement.
Akeycomponentinprojectandprogrammanagementistimemanagement.Avarietyoftraditionaltechniqueshavebeenusedtodevelopprojectschedules,includingtheGanttchartbyHenryL.Gantt(Weber2004),criticalpathmethod(CPM)(Kelly1961),program(itactuallymeansproject)evaluationandreviewtechnique(PERT)(Malcolmetal.1959),andlinearschedulingmethod(e.g.,Johnston1981),etc.Ofthesetraditionaltechniques,PERTistheonlyonethatenablesaschedulertoaddressuncertaintyinaprojectschedulebyassociatingactivitydurationswithprobabilitydistributions.However,usingPERTtohandleuncertaintyhasbeencriticizedforthefollowingreasons:(1)historicaldatatosupportthedevelopmentoftheprobabilitydistributionfunctionsoftheactivitydurationsisusuallyunavailable(HerroelenandLeus2005),and(2)itdoesnotexplicitlyaddressthesourcesofuncer-tainty(Khodakaramietal.2007).Inrecentyears,severalnewtech-niqueshavebeenproposedtoaccommodateuncertaintyinprojectscheduling.Onetechniquethatgainspopularityisthecriticalchainscheduling(CCS)method,whichincorporatestaskdependencies,resourceavailability,andfourtypesofbuffers(project,feeding,resource,capacity)intoaprojectschedule(Goldratt1997).Inaddi-tion,HerroelenandLeus(2005)summarizedfiveapproachestodealingwithuncertainty:reactivescheduling(e.g.,SzelkeandKerr1994;SabuncuogluandBayiz2000),stochasticscheduling(DemeulemeesterandHerroelen2002),fuzzyscheduling(e.g.,SlowinskiandHapke2000),proactive(robust)schedu-ling(e.g.,Davenportetal.2001;MehtaandUzsoy1999),andsen-sitivityanalysis(e.g.,HallandPosner2004).However,thesefiveapproachesmainlydealwiththeuncertaintiesinactivityandprojectdurations,nottheuncertaintiesinthenetworkstructurethatdefinesthelogicalrelationshipsamongtheactivitiesorprojects.Conse-quently,althoughtheestimatedactivitydurationsareallowedtovary,thelogicalrelationshipsamongtheactivitiesarefixedandgovernedbythepredeterminednetworkstructure.Inconstruction
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Downloaded from ascelibrary.org by Tongji University on 10/12/15. Copyright ASCE. For personal use only; all rights reserved.literature,theuseofdifferentalgorithmstooptimizeconstructionscheduleshasbeendiscussed(e.g.,Oroujietal.2014),butthere-searchismainlybasedonapresumedprojectnetworkstructure.Thisisoftenundesirableforschedulingaconstructionprograminarealsituationwherethenetworkstructureitselfisalsosubjecttovaria-tionsduetotheaddition,removal,and/oradjustmentofproject/programcomponents.Therigidityofthenetworkstructurelimitsthepotentialoftheprogramscheduletoprovidemoreinsightfulandcomprehensiveinformationtodecisionmakersandimplementers.Forexample,aprogrammayconsistofmultipleprojectswithdiffer-entlevelsofimportance,dependentontheirrespectivecontributionstotheoverallprogramgoals.Whentheresourceortimebecomesinsufficienttosupportalltheprojects,theprogrammanagermaywishtoidentifyandimplementsomeprojectsorcertaincomponentsoftheprojectsthataremostessentialtotheprogramgoalsandsimultaneouslymaintainalogicalsequence.Inaddition,thepro-grammanagermaywishtoincludealternativeplans(PlanB)intheprogramscheduletoincreaseflexibilityinprogramimplemen-tation.Theexistingschedulingmethodsleavemuchtobedesiredintheseaspects.
Thispaperisbasedontheauthors’involvementinandreflectiononthemanagementofthefacilityconstructionprogramforthe2010ShanghaiWorldExpo.Theprogramconsistsofhundredsofprojectsandtensofthousandsofactivities.Ahierarchicalnet-workschedulingapproachwasusedtomanagetheprogram’sschedule.Inthehierarchicalstructure,theprogramschedulewasdividedintoseverallayersandthedegreeofdetailforthescheduleincreasedfromthetoplayertothebottomone.Ateachlayer,tradi-tionalschedulingtechniquessuchastheGanttchartandCPMschedulingmethodswereused.However,thetraditionaltechniquesdonotprovidesufficientflexibilitytohandlevariationsinprojectimportance,uncertaintiesandcontingenciesforprogramplanningandcontrol,especiallyattheearlystageofprogramdevelopment.Thispaperproposesanewschedulingtechniqueforprograms.Thetechniquemakesitpossibletoevaluatetherelativeimportanceofprojectswithinaprogramand/ortherelativeimportanceofactiv-itieswithinaproject;italsoenablestheinclusionofalternativesintheoverallprogramschedule.
Background
CPMiswidelyusedinconstructionprojectscheduling.However,thereareseverallimitationsontheuseofCPMtoschedulecomplexconstructionprograms.Theselimitationsarediscussedasfollows.First,CPMdoesnotshowtheintrinsicimportancelevelofpro-gram(project)activities.Aprogramcomprisesmultipleprojectsand/orsubprograms,butnotallofthemareequallyimportantwithrespecttotheircontributionstotheoverallprogramgoals(e.g.,so-cialandfinancial).Suchvariationsinimportanceattheprojectorsubprogramlevelwillpassontotheactivities,makingthemvaryinimportance,too.However,inaCPMschedule,theimportanceoftheactivitiesisbasedontheirfloats—theamountoffreetimethattheactivitiespossesswithoutaffectingtheoverallprojectduration.Whenresourceortimeisconstrained,prioritieswillbeassignedtoactivitiesonthecriticalpathorwiththefeweramountsoffloats.Therefore,whenusingCPMforprogramscheduling,aproject,whichistheleastimportantintheoverallprogramintermsofitscontributiontotheessentialprogramfunctionsandgoals,maybecomecriticalsolelybecausetheproject’sactivitieshavezerofloat.Thismakesitdifficultfortheprogrammanagertoiden-tifyandtrackthetrueprioritiesintheprogram.
Secondly,uncertaintiesandalternativesaredifficulttoincorpo-rateintoaprogramschedule.Theuncertaintiesmayarisefrom
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severalsources(HerroelenandLeus2005),including:ambiguousdefinitiononprogram/projectscopes,inaccurateestimateofactiv-itydurations,availabilityoffundingorresources,andweatherconditions,orothercontingencies.Thedeepercausesoftheuncertaintiesmayincludeignorance,lackofinformationorlackofcontrol(Chang2002).Althoughdifferentapproacheshavebeenproposedtoreduceuncertainties,suchastheearlyinvolvementofcontractorsinprojectdevelopment(Songetal.2009),manyuncer-taintiesstillexist.Forexample,intheShanghaiExpoconstructionprogram,thesitewasalreadyunderconstructionbeforethesche-maticdesignofthelandmarkbuilding,theChinaPavilion,wasstarted.Someprojectsremainedundecideduntilthelateverystageofprogramimplementationduetofundingissues.Suchuncertain-tiesduringtheimplementationstageoftheprogramcreatechal-lengesinplanningandscheduling.Ontheotherhand,theseuncertaintiesmakeitimportanttoaddcertainflexibilitytothepro-gramschedule,suchasalternativesolutions.Itiscriticallyimpor-tanttofindamechanismtoincorporatetheuncertaintiesandalternativesintotheprogramschedule.
Thirdly,becauseoftheirlimitationsinhandlingprioritiesandalternatives,CPMdoesnotprovidesufficientinformationforsensitivity-basedprogramevaluationandcontingencymanage-ment.Inevaluatingandplanningprograms,thedecisionmakersneedtodefinethescopes,weighthetrade-offsbetweendifferentalternatives,andidentifyandupdatethedemandforresourcesandtheiravailability.Thus,therearemanywhat-ifquestionstoaskduringthisprocess.Attheplanningstage,itwouldhelpdecisionmakerseffectivelyanswerthequestionsaboveiftheprogramschedulecanprovidecostandtimeinformationwithrespecttodifferentassumptionsandoptions.Attheimplementationstage,contingenciesmayariseinconstruction,includingtimedelays,significantcostoverruns,orfundingshortages.TheinfluenceofthesecontingenciesonaprogrammaybeillustratedinFig.1.Theplannedprogram,asshownintheleftsideofFig.1,hasagroupofdirectlyorindirectlyconnectedprojectsaswellasacer-tainfundinglevelanddurationassociatedwiththeprogram.Astheprogramproceeds,timeandcostoverrunsorfundingreductionsmaymakeitnecessarytochangetheoriginalscopeoftheprogram,iftheprogramstillneedstobecompletedwithintheoriginalbudgetandtimeframe.Therefore,theprogrammanagerwillhavetode-cidewhichprojectsorprojectcomponentsshouldbeadjusted,trimmed,oreveneliminated.Theimpactsofsuchadjustmentsonaprogramscheduleneedtobecarefullyreviewed.
ProposedProcessforDevelopingProgramSchedules
Withtheseissuesinmindandtheauthors’experienceofmanagingtheShanghaiExpoconstructionprogram,anewtechniquefor
Fig.1.Effectsoffundingreduction,time,andcostoverrunsonprogramschedule
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programschedulingisproposed.Theproposedtechniqueconsistsofthefollowingsteps:
1.Definitionoftheimportancelevelsofprojectsandtheiractivities;
2.Identificationofthelogicrelationshipsbetweentheactivities;3.Computationoftheprogramschedule;
4.Analysisandoptimizationoftheprogramschedule;and5.Updateoftheprogramschedule.
Implementationofthesestepsrequiressixpropositionsthatmustbesatisfied.OneofthepropositionsispresentedinStep1—importanceleveldefinitionforprojectsandtheiractivities.TheremainingfivepropositionsarepresentedinStep3—computationoftheprogramschedule.Thestepsandpropositionsarediscussedasfollows.
Downloaded from ascelibrary.org by Tongji University on 10/12/15. Copyright ASCE. For personal use only; all rights reserved.discussedlater.TheconventionaldiagramsusedinCPMmayberevisedtoindicatetheactivities’importancelevels.Fig.2showstwopossiblewaysofrepresentingtheimportanceofanactivity.Inthefigure,alowernumberisassumedtorepresentahigherimportancelevel.
Step2:IdentificationofLogicRelationshipsbetweenActivities
Alltheactivitiesinaprogramscheduleshouldbeconnectedtootheractivities.Aconnectionmaybeestablishedbetweentwoac-tivitiesthatbelongtoasameprojectorthatbelongtodifferentproj-ects.However,becausemostprojectsinaprogramaretypicallyimplementedindependently,extensiveconnectionsbetweentheprojectsarenotexpected.Iftherearealargenumberofinterprojectconnections,thetwoormultipleprojectsmaybemergedintoone.Besidesthecommonlyuseddeterministicconnectionsbetweentheactivities,anothertypeofconnection,optionalconnection,isusedintheproposedschedulingmethod.Anoptionrepresentsaprojectcomponent,aconstructionmethod,oranentireproject,whichcanbereplacedbyitsalternative(s)withoutseriouslyaffect-ingtheprogram’scoreobjectives.Forinstance,eitherafootbridgeoranundergroundtunnelmaybeafeasiblealternativetofacilitatetrafficflowinaparticulararea.Althoughbothalternativescanmeetthesamefunctionalrequirements,theireffectsonprojecttimeandcostmaybedifferent.ThediagraminFig.3illustrateshowtheoptionsoralternativescanberepresentedinaprogramschedule.Step3:ComputationoftheProgramSchedule
Theproposedschedulingmethodintegratesalternativesandactiv-itieswithdifferentlevelsofimportanceintoaconventionalCPMschedule.Thecalculationmethodforthisnewnetworkisdemon-stratedbyanexampleinFig.4.Thesameconventionsfortheprecedencediagramareadoptedinthisnetwork,withnodesrepresentingactivitiesandarrowsrepresentinglogicalrelation-ships.Tosimplifythediscussion,therelationshipsbetweentheactivitiesareassumedtobefinish-to-start.Unliketheconventionalprecedencediagram,however,Fig.4includesprojectalternativesandactivityimportanceinformationthatisderivedfromthepre-vioussteps.ItisassumedthattheprogramshowninFig.4consistsoffiveprojectswiththreeimportancelevels.Initially,alltheactiv-itiesthatbelongtoacertainprojecthavethesamelevelofimpor-tance.Inaddition,attheprojectlevel,Projects4and5aretwoexchangeablealternativesthatmayequallysatisfythekeyprogramobjectivesorfunctions.Attheactivitylevel,ActivitiesG3andH3inProject3arealsoexchangeablealternatives.Thealternativeproj-ectsoractivitiesaredesignatedbythecirclesinFig.4.Theinclu-sionofsuchinformationaffectstheCPMcalculationmethod.Itisfoundthat,inordertocarryoutlogicalcalculation,Propositions
Step1:DefinitionoftheImportanceLevelsforProjectsandTheirActivities
Techniquesforrankingandprioritizingprojectsarewidelystudiedinexistingliterature(e.g.,Figueiraetal.2005).Projectscanbeevaluatedbasedonasinglecriterionorasetofcriteria.Anexampleofthesinglecriterionistheeconomicreturnintermsofthenetpresentvalue,benefit-cost-ratio,rateofreturn,orothers.Examplesofmulticriteriadecision-making(MCDM)methodsincludegoalprogramming(e.g.,Figueiraetal.2005),analytichierarchyprocess(e.g.,Saaty2005),andothers.Basedontheevaluationresults,agroupofprojects,perhapswithdifferentrankingscores,arese-lectedtoentertheprogram.Duringtheprojectselectionstage,theinterdependenciesbetweentheprojectsalsoneedtobeconsid-ered.Inspiteoftheevaluationmethodsused,eachprojectorsub-programshouldhaveimplicitorexplicitlevelofimportanceattheendoftheevaluationperiod.Suchinformationis,however,oftenlostlateronwhentheprogramscheduleisdeveloped.Oneobjec-tiveofthisproposedschedulingtechniqueistoretaintheprojectrankinginformationintheschedulingprocess.
Proposition1
Thechosenprojectsandsubprogramsinaprogramscheduleinheritthelevelsofimportancefromtheprogramdefinitionstage,andallthescheduledactivitiesinitiallyhavethesamelevelofimportanceasthemainprojectsorsubprogramstowhichtheybelong.
Theimportanceofaprojectorsubprogrammaybeinitiallydes-ignatedbyanumericalrankingscore,whichneedstobeconvertedtoadiscreteimportanceleveltosimplifyschedulingcalculation.Thescheduledactivitiesinitiallyinheritthesamelevelofimpor-tancefromtheproject,buttheimportanceoftheactivitiesmaybechangedinthesubsequentschedulingprocess,aswillbe
(a)
(b)
Fig.2.Representationofactivitieswithdifferentimportancelevels:(a)useofdifferentlinestylestoshowimportancelevelofanactivity;(b)useofanumberattherightuppercorneroftheactivityboxtoshowimportancelevelofanactivity
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Fig.3.Graphicalrepresentationofalternatives
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Downloaded from ascelibrary.org by Tongji University on 10/12/15. Copyright ASCE. For personal use only; all rights reserved.Fig.4.Exampleofprogramschedule
2–6mustbesatisfied.Eachofthepropositionsisdescribedasfollows.
Proposition2
Aprogramhasasinglestartactivityandasingleendactivity.Thispropositionistodifferentiateaprogramfromanongoing,routineoperation.ItisalsoanimportantassumptiontoapplytheCPMschedulingtechniquestoprogramscheduling.Iftheprogramhasnoendactivity,itisimpossibletocarryoutbackwardcalculation.
Proposition3
Anactivitymaypossessmultiplelevelsofimportancederivedfromconnectionswithotheractivities.Exceptforthelastactivity,theimportancelevelofanactivity’sprecedingactivity(oractivities)shouldbegreaterthanorequaltotheimportancelevelofthisactivity.
AllactivitieswithinthesameprojectinitiallyhavethesamelevelofimportanceaccordingtoProposition1;therefore,Propo-sition3ismainlyusedtogovernactivitieswithinterprojectrela-tionships.Fortwoactivitiesthathaveafinish-to-startrelationshipbutbelongtotwoprojects,theymayhavedifferentimportancelev-els.Iftheprecedingactivityismoreimportantthanthesucceedingactivity,noproblemwillarise.However,iftheprecedingactivityislessimportantthanthesucceedingactivity,itwillcauseaproblem.Forexample,ifthelessimportantprojectiscanceledorpostponed,thepreceding-succeedingrelationshipwillmakethesucceedingactivityinthemoreimportantprojectunableorlatetostart,thusdegradingtheimportancelevelofthesucceedingactivityanditsassociatedproject.Tofixtheproblem,theimportancelevelofthepredecessor(s)needstobeupgraded.
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Thelastactivityintheprogramscheduleistypicallyacombi-nationofseveralactivitiessuchastheterminationoftheprojectswiththefirst-levelimportance,terminationoftheprojectswiththesecond-levelimportance,etc.Hence,whentheseactivitieswithdifferentlevelsofimportancearecombinedintoonesingleendac-tivity,notallofitspredecessorshavetobeatthesamehighestlevelofimportance.Therefore,thelastactivityisexemptedfromthiscondition.
Itisagoodpracticetodifferentiatetheinheritedimportancelevelfromtheimportancelevelcausedbyinterprojectconnections,namedasthederivedimportanceinthispaper.Thederivedimpor-tancehastwoattributes:animportancelevelandtheactivity(activities)fromwhichtheimportancelevelisderived.Thelevelofthederivedimportance,comingfromthesuccessorofanactivity,shouldbehigherthanorequaltotheinheritedimportance.Forex-ample,inFig.4,ActivityE3inProject3issucceededbyActivityC2inProject2.BecauseC2hasanimportancelevelhigherthanthatofE3,theimportancelevelsofC2andallitsdirectandindirectpredecessorsinProject3shouldbeupgraded.Otherwise,ifthelessimportantProject3iscancelled,Project2willbeaffectedbecauseE3isoneoftheimmediatepredecessorsofC2.Therefore,someactivitiesthatareinitiallyassignedwithalowimportancelevelmayneedtobeupgradedbecausetheyarethepredecessorsofthemoreimportantactivities.Upgradingonlyrequirestheincreaseoftheimportanceleveloftheconcernedactivitytothesamelevelasitsimmediatesuccessor,orthehighestimportancelevelofallitsimmediatesuccessors.Whenanactivityissucceededbyanop-tionalactivitywithhigherimportance,theactivityfromwhichthederivedimportanceisobtainedshouldalsoberecorded.Forexample,G3inProject3issucceededbyA4inProject4and
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A4ismoreimportantthanG3initially;therefore,thederivedim-portanceofG3shouldbeadjustedtoahigherlevel.However,sinceA4isoptional,thederivedimportanceofG3isnotdefinitiveandthesourceofthederivedimportanceneedstobemarked.Proposition4
Anactivitywithacertainimportancelevelmustbesucceededbyatleastoneactivitythathasthesameorhigherimportancelevelasitself.
Thisisnamedasthepass-through-the-endruleinthispaper.Theruleisalsomainlyusedtogoverninterprojectconnections.Thepurposeistoensuretheintegrityoftheprogram.Forexample,inFig.4,Project1isfollowedbyeitherProject4or5ofthesameimportancelevel;iftheimportancelevelsofProjects4and5arereducedandsubsequentlyremoved,ActivityF1willbecomeadan-glingactivitythatconnectstonowhere.IfProject1isindeedin-dependentandcanfulfillitsroleintheprogramwithoutProject4or5,adirectconnectionbetweenActivityF1andthelastactivityoftheprogramshouldbeadded,tologicallyclarifythatProject1isindependent.
Proposition5
Exceptforthefirstandlastactivities,acompulsoryactivitymusthaveatleastonelogicallycompulsorypredecessorandatleastonelogicallycompulsorysuccessor.
Becausealternativesareintroducedintothenetwork,itneedstobeassuredthatthecompulsoryactivitiesdonotlosetheirprede-cessor(s)andsuccessor(s)duetotheremovaloftheoptionalactiv-itiesorprojects,exceptforthefirstactivity,whichdoesnothaveapredecessor,andthelastactivity,whichdoesnothaveasuccessor.Thelogicallycompulsorydoesnotnecessarilyrequirethattheac-tivityconnectstoanactualcompulsoryactivityoractivities.Aslongastheprecedingandsucceedingrelationshipsarelogicallyaffirmed,itmeetstherequirement.Forexample,ActivityC3inFig.4issucceededbyeitherG3orH3,whichisoptional.However,becauseoneofthemwillhavetobethesuccessorofC3,C3stillhasalogicallycompulsoryactivityasitssuccessor.Ontheotherhand,thecompulsoryActivityD3inProject3isthepredecessorforActivityH3,whichisanoptionalactivity.IfH3isremovedinfavorofG3,D3willbecomeadanglingactivityunlessitisconnectedtoanotheraffirmativeactivitysuchasI3.
Proposition6
Mutuallyexclusiveprojectsandactivitiesshouldhavethesamelevelofdirectimportance.
Theimportancelevelsofactivitiesdependontheimportancelevelsofprojectsorprojectcomponentsuponwhichtheactivitiesarebased.Ifmutuallyexclusivealternativesareusedtomeetthesameneeds,theyshouldhavethesamelevelofimportance.ThisconditionistoensuretheexchangeabilityofthealternativesandnonviolationofProposition4.InFig.4,assumethatProject5hasalowerimportancelevelthanProject4andProject5ischoseninfavorofProject4(alternativeimpliesthateitheroneofthemcanbechosen).ActivityF1inProject1willconnecttoanactivitythathasalowerimportancelevel,henceviolatingProposition4.Basedonthepropositionsabove,theexampleprogramscheduleshowninFig.4canbecalculatedbythefollowingsteps:
1.Specifythealternativesintheprogram.Uniqueidentificationcodesmaybeassignedtothealternatives.Inthispaper,analternativeattheprojectlevelisrepresentedbyitsprojectnumber,suchasP4andP5,whileanalternativeactivitywithinaprojectisrepresentedbytheprojectnumberfollowedbyanarbitrarycode(e.g.,P3-a1).
2.Updatetheimportancelevelsofactivitiescausedbyinterpro-jectconnections,i.e.,thederivedimportancenamedinthis
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Downloaded from ascelibrary.org by Tongji University on 10/12/15. Copyright ASCE. For personal use only; all rights reserved.paper.Forexample,E3hasanimportancelevelofIII,butbe-causeitisthepredecessorofC2withanimportancelevelofII,E3andallitspredecessorsneedtobeupgradedtoanimpor-tancelevelofII.Ifthederivedimportanceiscausedbyanalternative,thealternativecodealsoneedstobeincluded.Forexample,ActivityC3hasderivedimportanceatLevelIcausedbytheconnectionbetweenG3andProject4;hence,thede-rivedimportanceforC3iswrittenasI(P3-a1)(P4),inwhichthefirstlettershowstheimportancelevelandthelettersintheparenthesesshowthealternatives.
3.Calculatetheearlystart(ES),earlyfinish(ES),latestart(LS),andlatefinish(LF)ofalltheactivitiesbasedontheconven-tionalCPMmethod.Thecalculationneedstotakethealternativesandimportancelevelsoftheactivitiesintoconsideration.UsingthesameexampleillustratedinFig.4,theforwardandbackwardpathcalculationsforProject4andaportionofProject3ispresentedinFig.5.TheforwardpathcalculationisstraightforwardexceptforthoseactivitiesinProject4.BecausetheearlystarttimeoftheactivitiesinPro-ject4iscontrolledbythealternativea1inProject3,thealter-nativenumberP3-a1needstobelabeled.Whenperformingthebackwardpathcalculationfromtheend,therearethreemajorscenarios:(1)tocompleteonlyprojectsofthefirstim-portancelevel;(2)tocompleteprojectsofthesecondimpor-tancelevelandabove;and(3)tocompleteprojectsofthethirdimportancelevelandabove.Scenario(1)includestwooptions:toimplementProject4orProject5.Scenario(2)alsoincludesthesametwooptions.Scenario(3)includesthreeoptionstoimplement:Project5andAlternative1(a1)inProject3,Pro-ject5andAlternative2(a2)inProject3,andProject4andAlternative1(a1)inProject3[Becausea1isthepredecessorofA4inProject4,Alternative2(a2)cannotbechosenifPro-ject4isselected].Inthisparticularexample,theadditionofthethirdimportance-levelprojectdoesnotincreasetheoverallprogramdurationfromtheschedulethatonlyconsistsofthefirstandsecondimportance-levelprojects.ActivitiesinProject4havetwosetsoflatestart/finishtimesasshowninFig.5,dependingontheimportancelevelsofprojectstocomplete.ThelatefinishtimeofActivityG3iscontrolledbythelatestarttimeoftwosuccessors,A4andI3,whichcanbederivedfromthefollowingequation:
89<10ðP4ÞðIÞ=
LatefinishG3¼min11ðP4ÞðIIÞðIIIÞ
:;
28ðIIÞðIIIÞ
98
10ðP4ÞðIÞ>>=<
11ðP4ÞðIIÞðIIIÞ
¼min
>;:28ðP4ÞðIIÞðIIIÞ>28ðP5ÞðIIÞðIIIÞ89<10ðP4ÞðIÞ=¼11ðP4ÞðIIÞðIIIÞ:;28ðP5ÞðIIÞðIIIÞ
ð1Þ
InEq.(1),thelatefinishtimeofG3isderivedfromthethird-levelactivityI3andisnotdependentonaspecificAlternativeP4orP5,whilethelatefinishtimederivedfromActivityA4isonlybasedonAlternativeP4.Forcomparisonpurposes,thelatefinishtime28(II)(III)needstobespecifiedastwooptions:28(P4)(II)(III)and28(P5)(II)(III).WhencompletingalltheimportancelevelII/IIIactivities,ifP4ischosen,thelatefinishofActivityG3willbe11(thesmallervalueof11and28);ifP5ischosen,thelatefinishtimeofG3willbejust28.AscanbeseeninFig.5,differentpossiblecombinationsgeneratedifferentsetsoflatestart/finishtime,which
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Downloaded from ascelibrary.org by Tongji University on 10/12/15. Copyright ASCE. For personal use only; all rights reserved.Fig.5.Examplecalculationoftheprogramschedule
providesimportantinformationforaprogrammanagertoweightheoptions.
Step4:AnalyzeandOptimizetheProgramScheduleThecalculationresultsoftheentireprogramscheduleinFig.4aresummarizedandshowninTable1.Foreachactivity,thetableshows:(1)theprojecttowhichtheactivitybelongs,(2)theinitialactivityimportancelevelthatisinheritedfromtheprojectimpor-tanceleveldeterminedattheplanningstage,(3)thederivedimpor-tancelevelcausedbyinterprojectconnections,(4)alternativecode,and(5)theCPMtimes(ES,EF,LS,LF)andtotalfloat.UnliketheconventionalCPMschedule,theactivitytimesalsoshowthealter-nativesandimportancelevelsthatareassociatedwiththecalculatedresults.TheinformationinTable1maybeusedtoanalyzeandoptimizetheprogrambasedonfundingandtimeconstraints.First,theresultsprovidethetotaldurationsoftheprogramindifferentscenarios.Forexample,ifonlythefirst-levelprojectsareimplementedandAlternativeP5ischosen,thetotaldurationoftheprogramis19.IfAlternativeP4isexecuted,thetotaldurationbecomes32.Ifthesecond-levelprojectisimplemented,thetotaldurationis33,andtheinclusionofthethird-levelprojectwillnotfurtherincreasetheprogramduration.Theprogrammanagercanchoosetherightcombinationofprojectsandalternativestomeetthetimeobjective.
Secondly,foreachindividualactivity,itsinheritedimportancelevel,theimportancelevelcausedbyinterprojectconnections,anditsconnectionwithotheractivitiesorprojectscanbeclearlyseen.Inaddition,thecalculationgeneratesthestartandfinishtimesandfloatsofactivitieswithrespecttodifferentimportancelevelsandalternatives.Suchinformationprovidesprogrammanagersthedeadlinesofchoosingandimplementingtheprogramactivitiesinresponsetodifferentscenarios.Forexample,ifonlyprojectswithimportanceLevel1areconsideredandProject4andthefirstalternativeinProject3arechosen,C3inProject3needstostartonDay2withnofloat.Ifprojectswithallthelevelsofimportanceare
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consideredandthefirstalternativeinProject3(P3-a1)andProject4arechosen,thelatestarttimeforC3isDay3,withonedayoffloat.IfprojectswithalltheimportancelevelsareconsideredandP3-a1andProject5arechosen,thelatestarttimeforC3isDay20,with18daysoffloat.Ifprojectswithallimportancelevelsarecon-sideredandP3-a2ischosen,thelatestarttimeforC3isDay22,with20daysoffloat.
Thirdly,iftheactivitiesareloadedwithcostinformation,theprogramcostsofimplementingprojectsofdifferentimportancelevelsandalternativescanbeeasilycalculatedandsubsequentlyevaluated.Suchinformation,combinedwithtimeinformation,canassistdecisionmakersinidentifyingprojectsandalternativesthatsatisfytheprogram’skeyobjectiveswithoutexceedingthebudget.Theintegrationoftimeandcostsarebelievedtobeessen-tialforprojectsuccess(e.g.,Choetal.2010).
Fourthly,theprogramschedulehighlightstheportionofaprojectthatismoreimportantthantherestpartofthesameprojectcausedbyinterprojectconnections.Forexample,theimportancelevelsofActivitiesB3andE3areinitiallythelowest,butbecausetheyarepredecessorsofActivityC2inanotherproject,theirim-portancelevelsareupgradedtoLevelII.IfabudgetcutcausestheLevelIIIprojecttobeterminated,atleastB3andE3shouldbekept.Suchasituationisnotuncommoninaconstructionprogram.Forinstance,assumethatoneoftheprojectsinaprogramistobuildacitysquarewithsculpturesandfountainsaswellasnewbuildings.Budgetconstraintsmayplacethesculptureandfountainportionsoftheprojectsonhold,butthesiteconstructionandundergroundutil-itiesmayremainunchangedbecausetheyareessentialforthenearbybuildings.
Step5:UpdateProgramSchedule
TheprogramscheduleasshowninFig.4needstobefrequentlyupdatedtopromptlyreflecttheprogressandchangesinthepro-gram.Astheprogramproceeds,itsoonlosessomeflexibilityandoptions.Forexample,onceA5inProject5isstarted,all
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ActProjectOrginalimportanceA11IB11IC11ID11IE11IF11I04014098-7
A2B2C2D2E2F2A3B3C3222222333IIIIIIIIIIIIIIIIIIIII//////III(P3-a1)(P4)IIIIII(P3-a1)(P4)/////////071514232702271423242733286 J. Manage. Eng., 04014098
D3E3F3G3IIIIII///////P3-a2/P4P4P4P5P5P5/72110(P3-a1)14(P3-a1)28(P3-a1)7111519(P5)(I)32(P4)(I)33(II)(III)3333IIIIIIIIIIIIIIIIIIIII(P3-a1)(P4)///P3-a128156715211092614(P3-a1)28(P3-a1)32(P3-a1)11151919(P5)(I)32(P4)(I)33(II)(III)H3I3A4B4C4A5B5C5END33444555/IIIIIIIIIIIII3(P4)(I);4(P4)(II)(III)0(P5)(I);14(P5)(II)(III)3(P4)(I);4(P4)(II)(III)0(P5)(I);14(P5)(II)(III)4(P4)(I);5(P4)(II)(III)1(P5)(I);15(P5)(II)(III)6(P4)(I);7(P4)(II)(III)3(P5)(I);17(P5)(II)(III)7(P4)(I);8(P4)(II)(III)4(P5)(I);18(P5)(II)(III)9(P4)(I);10(P4)(II)(III)6(P5)(I);20(P5)(II)(III)310151723270(P3-a1)(P4)(I)0(II)(III)2(II)(III)2(P3-a1)(P4)(I)3(P3-a1)(P4)(II)(III)20(P3-a1)(P5)(II)(III)22(P3-a2)(P5)(II)(III)23(P3-a1)21(P3-a2)8(II)(III)226(P4)(I)7(P4)(II)(III)24(P5)(II)(III)262810(I)11(II)(III)14(I)15(II)(III)28(I)29(II)(III)7(I)21(II)(III)11(I)25(II)(III)15(I)29(II)(III)19(P5)(I)32(P4)(I)33(II)(III)6(P4)(I);7(P4)(II)(III)3(P5)(I);17(P5)(II)(III)6(P4)(I);7(P4)(II)(III)3(P5)(I);17(P5)(II)(III)6(P4)(I);7(P4)(II)(III)3(P5)(I);17(P5)(II)(III)9(P4)(I);10(P4)(II)(III)6(P5)(I);20(P5)(II)(III)9(P4)(I);10(P4)(II)(III)6(P5)(I);20(P5)(II)(III)10(P4)(I);11(P4)(II)(III)7(P5)(I);21(P5)(II)(III)1017232727332(P3-a1)(P4)(I)2(II)(III)8(II)(III)6(P3-a1)(P4)(I)7(P3-a1)(P4)(II)(III)24(P3-a1)(P5)(II)(III)26(P3-a2)(P5)(II)(III)28(P3-a1)26(P3-a2)15(II)(III)2810(P4)(I)11(P4)(II)(III)28(P5)(II)(III)283314(I)15(II)(III)28(I)29(II)(III)32(I)33(II)(III)11(I)25(II)(III)15(I)29(II)(III)19(I)33(II)(III)19(P5)(I)32(P4)(I)33(II)(III)3(P4)(I);4(P4)(II)(III)0(P5)(I);14(P5)(II)(III)3(P4)(I);4(P4)(II)(III)0(P5)(I);14(P5)(II)(III)4(P4)(I);5(P4)(II)(III)1(P5)(I);15(P5)(II)(III)3(P4)(I);4(P4)(II)(III)0(P5)(I);14(P5)(II)(III)4(P4)(I);5(P4)(II)(III)1(P5)(I);15(P5)(II)(III)3(P4)(I);4(P4)(II)(III)0(P5)(I);14(P5)(II)(III)3303000(P3-a1)(P4)(I)0(II)(III)0(II)(III)0(P3-a1)(P4)(I)1(P3-a1)(P4)(II)(III)18(P3-a1)(P5)(II)(III)20(P3-a2)(P5)(II)(III)21(P3-a1)19(P3-a2)0(II)(III)70(P4)(I)1(P4)(II)(III)18(P5)(II)(III)1970(I)1(II)(III)0(I)1(II)(III)0(I)1(II)(III)0(I)14(II)(III)0(I)14(II)(III)0(I)14(II)(III)J.Manage.Eng.
Note:Act=activitycode;Alt=codeforalternatives;Der.Imp=derivedimportancelevel;EF=earlyfinish;ES=earlystart;LF=latefinish;LS=latestart;Org.Imp=originalimportancelevel;Pro=projectnumber;TF=totalfloat.Fig.6.Multilevelhierarchicalnetworkschedule
Downloaded from ascelibrary.org by Tongji University on 10/12/15. Copyright ASCE. For personal use only; all rights reserved.theactivitiesinProject4needtoberemoved.Theconnectionsbe-tweenProject4andProject3willalsoberemoved.Besidesthedecisionsonalternatives,theremaybeotherchangesinthepro-gramschedulesuchaschangesinactivitydurations,importancelevels,andlogicalconnectionsbetweentheactivities.Allthechangesneedtobeincorporatedintotheupdatedprogramsched-ule,followedbyrecalculatingthenetworkschedule.
ApplicationoftheProposedSchedulingMethod
HallmarkeventssuchastheOlympicsandWorldExpoareoftenusedbycountriesorlocalgovernmentsasopportunitiestoboosteconomyandurbanredevelopment(EssexandChalkley1998).Thesuccessofthehallmarkeventsisaffectedbythecostsanddeliverytimeoftheinfrastructuresbuilttosupportsuchevents.Facilityconstructionofthistypeusuallyinvolvesalargenumberofinterrelatedprojects.Therefore,theseprojectsarebettertobemanagedasaprogram,insteadofasinglemegaproject.Suchpro-gramsareusuallypubliclyfundedorsubsidizedandhenceaffectedbypublicfinancingproceduresandregulations,macroeconomicconditions,andeventhepoliticalenvironment.Therearealsomul-tiplestakeholdersinvolvedintheprograms.Forexample,fortheShanghaiWorldExpo,alargenumberofbuildingswerefundedbyforeigncompaniesanddesignedandconstructedbyforeigncoun-tries.Thesecharacteristicsmaketheprogramssubjecttonumerouschangesanduncertainties,yettheprogramsstillhavefixeddead-linessetbytheevents.Therefore,integratedtimeandcostmanage-mentoftheseprogramsposesachallengeforprogrammanagers.AhierarchicalnetworkasshowninFig.6wasusedtoscheduletheconstructionprogramforthe2010ShanghaiWorldExpo.AtLevelI,thecontrollingstartandcompletiondateswerespecifiedformajorprojectsandsubprograms,whichwerederivedfromtheworkbreakdownstructure(WBS).AtLevelII,theschedulesforprojectsandsubprogramswereexpandedtoincludemajormile-stones.AtLevelIII,comprehensiveschedulesweredevelopedforeachzoneoftheprogram.AtLevelIV,detailedschedulesweredevelopedforeachprojectorsubprogram.Althoughsequentialre-lationshipsweredevelopedfortheschedulesatLevelsII,III,andIV,respectively,theserelationshipswerenotmappedtoschedulesatdifferentlevels.Asaresult,schedulechangeatacertainlevelwasnotautomaticallyreflectedintheentireprogramschedule.Incorporatingoptionsandimportancelevelsintotheprogramschedulecouldcreateflexibilityformoreefficientmanagement,helpingaddressvariouschallengesincludingcomplexscope,fixeddeadline,andconstraintbudget.Forinstance,theprogramcostandschedulemayhavebeenbettermanagediftheprojectswereas-signedwithdifferentimportancelevels,basedontheircontribu-tionstothekeyprogramgoals.TheShanghaiWorldExpoprogramhadmultiplegoalswithdifferentpriorities.Asmentionedpreviously,multicriteriadecisionanalysis(MCDA)techniques
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couldhavebeenusedtoranktheprojectsundertheprioritizedpro-gramgoals.Therankingscorescouldthenbeusedtohelpdeter-minetheimportancelevelsoftheprojects.Forexample,oneprojectintheprogramwastobuildtwoVIPferryterminalswithaplanneddurationofmorethanoneyear.ComparedtomanyotherprojectssuchastheExpoThemePavilion,theferryterminalswerelessim-portant.Whentimeandfundingbecametight,asoccurredattheendoftheExpoconstructionprogram,prioritywasgiventoproj-ectsthatservedthecorefunctionsoftheprogram.However,projectswithlowpriority,oraportionoftheprojectswithlowpri-ority,becamenecessarybecauseofinterprojectconnections.Theproposedtechniquewouldmakeiteasytoexaminethesensitivityoftheprogramdurationsandcoststotheinclusionorremovaloftheterminalconstructionproject.Inaddition,time,floats,andcon-nectionsbetweentheindividualactivitiesfortheprojectscouldhavebeeneasilyretrieved.
Duetothesizelimitofthepaper,theentirescheduleoftheShanghaiWorldExpoconstructionprogramisnotincluded.TwoprojectsinFig.7areusedtoconceptuallyillustratethefea-sibilityofincorporatingoptionsandimportancelevelsinprogramscheduling.OneoftheprojectsistheconstructionoftheChinaPavilionandtheotheristheconstructionofthetransportfacilitiesneartheChinaPavilion.First,differentimportancelevelsareas-signedtothetwoprojects.Secondly,optionswereaddedtothetwoprojectsandtheimpactsoftheoptionsonprogramscheduleandcostareassessedaccordingly.Forexample,theupperstructureoftheChinaPavilioncouldbebuiltwithsteelorconcrete.Ifthesteelstructurewereused,itwouldneedalongerleadtimeforthedevelopmentofshopdrawings,fabrication,andtransportationofthestructuremembers,eventhoughthisprocesscouldbecarriedoutparallelwithotheractivities.Oncethesteelmemberswerede-liveredtothesite,theycouldbeassembledandbeliftedbycranes.Thiscouldpotentiallyacceleratetheprojectscheduleincompari-sontoconcreteconstruction.However,assemblyofthesteelstruc-turesrequiredoccupyingthesitewherethetransportprojectwaslocated,whereastheuseoftheconcretestructuremightnotrequirethisspace.ByaddingthesetwooptionsandperformingCPMcal-culation,theeffectsoftheoptionsontime,costs,andotherprojectsmaybeassessed.Similarly,aportionofthetransportationfacilitiesthataccommodatepedestrianscrossingtheroadmayhavethreeoptions:anundergroundtunnel,afootbridge,orjusttrafficlights.Thesevariousoptionsresultindifferentprogramcostandduration,asshowninTable2.
Theinclusionofoptions,interprojectconnection,andimpor-tanceinformationintheprogramschedulemayalsohelpoptimizetheuseofresources.IntheShanghaiExpoconstruction,morethan400newbuildingswereconstructedinashortperiodoftime.Ifmostbuildingsusedconcretestructures,thelocalready-mixedcon-creteplantsmaynothavethesufficientcapacityatthepeakcon-structiontime.Theproposedprogramschedulingtechniquecanbeusedtoanalyzetheamountofconcreteneededatdifferenttimeand
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Table2.SummaryofCalculationResultfortheScheduleinFig.7Importancelevel11222222
Alternative
ConcretestructureSteelstructureConcreteTunnelstructureTraffic
lightsFootbridge
SteelstructureTunnel
TrafficlightsFootbridge
Completiontime(week)
5950595959505050
Cost(million)84.590.5118.5115.5117.5116.5113.5115.5
Thediscussioninthispaperisbasedonsomesimplifiedexamples,andtherelationshipsbetweentheactivitiesareallfinish-to-startandnospecificlimitisimposedontheuseofresources.Theeffectsofrelaxingtheseassumptionsontheproposedmethodmaybefur-therstudied.
Acknowledgments
ThepaperissupportedbyaprojectattheHongKongPolytechnicUniversity(1-ZV8H).
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LackofaspecialmethodologytohandletheuniqueissuesandchallengesinconstructionprogramsistheAchilles’heelinpro-grammanagement.Oneparticularareathatneedstobeimprovedisthemanagementofpriorities,uncertainties,andinterprojectcon-nectionsinaprogramenvironment.Becausetimemanagementofprogramsisstilllargelydependentonthetechniquesdevelopedformanagingasingleproject,theinformationprovidedforprogrammanagersisquitelimited.
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